@article{Bajaj95,
 author = {Bajaj,, Chandrajit L. and Chen,, Jindon and Xu,, Guoliang},
 title = {Modeling with cubic A-patches},
 journal = {ACM Trans. Graph.},
 volume = {14},
 number = {2},
 year = {1995},
 issn = {0730-0301},
 pages = {103--133},
 doi = {http://doi.acm.org/10.1145/221659.221662},
 publisher = {ACM},
 address = {New York, NY, USA},
 }


@article {Blinn05,
    AUTHOR = {J. Blinn},
    TITLE = {Jim Blinn's Corner, How to Solve a Cubic Equation.},
    journal = {IEEE CG \& A},
    YEAR = {2007},
    volume = {27},
    issue = {3},
    pages = {78--89},
}

@INPROCEEDINGS {Bloomenthal94,
    author = {Jules Bloomenthal},
    title = {An implicit surface polygonizer},
    booktitle = {Graphics gems IV},
    year = {1994},
    isbn = {0-12-336155-9},
    pages = {324--349},
    publisher = {Academic Press Professional, Inc.},
    address = {San Diego, CA, USA},
 }

 @book{Bloomenthal97,
 editor = {Bloomenthal,, Jules and Wyvill,, Brian},
 title = {Introduction to Implicit Surfaces},
 year = {1997},
 isbn = {155860233X},
 publisher = {Morgan Kaufmann Publishers Inc.},
 address = {San Francisco, CA, USA},
 }

@article{Che05,
 author = {Che,, Xiangjiu and Liang,, Xuezhang and Li,, Qiang},
 title = {G1 continuity conditions of adjacent NURBS surfaces},
 journal = {Comput. Aided Geom. Des.},
 volume = {22},
 number = {4},
 year = {2005},
 issn = {0167-8396},
 pages = {285--298},
 doi = {http://dx.doi.org/10.1016/j.cagd.2005.01.001},
 publisher = {Elsevier Science Publishers B. V.},
 address = {Amsterdam, The Netherlands, The Netherlands},
 }

@BOOK {Dennis83,
    AUTHOR = {J.E. Dennis and Robert B. Schnabel},
    TITLE = {Numerical methods for unconstrained optimization and nonlinear equations},
    PUBLISHER = {Prentice-Hall Englewood Cliffs, N.J.},
    YEAR = {1983} }

 @article{DeRose93,
 author = {DeRose,, Tony D. and Goldman,, Ronald N. and Hagen,, Hans and Mann,, Stephen},
 title = {Functional composition algorithms via blossoming},
 journal = {ACM Trans. Graph.},
 volume = {12},
 number = {2},
 year = {1993},
 issn = {0730-0301},
 pages = {113--135},
 doi = {http://doi.acm.org/10.1145/151280.151290},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

 @inproceedings{Elber01,
 author = {Elber, Gershon and Kim, Myung-Soo},
 title = {Geometric constraint solver using multivariate rational spline functions},
 booktitle = {SMA '01: Proceedings of the sixth ACM symposium on Solid modeling and applications},
 year = {2001},
 isbn = {1-58113-366-9},
 pages = {1--10},
 location = {Ann Arbor, Michigan, United States},
 doi = {http://doi.acm.org/10.1145/376957.376958},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

@inproceedings{Hanrahan83,
 author = {Hanrahan,, Pat},
 title = {Ray tracing algebraic surfaces},
 booktitle = {SIGGRAPH '83: Proceedings of the 10th annual conference on Computer graphics and interactive techniques},
 year = {1983},
 isbn = {0-89791-109-1},
 pages = {83--90},
 location = {Detroit, Michigan, United States},
 doi = {http://doi.acm.org/10.1145/800059.801136},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

 @article {Harris07,
    AUTHOR = {Harris, M. and Owens, J. and Sengupta, S. and Zhang, Y. and Davidson, A.},
    TITLE = {CUDPP homepage},
    YEAR = {2007},
    NOTE = {http://www.gpgpu.org/developer/cudpp/}}
 }

@ARTICLE{Hart96,
    author = {John C. Hart},
    title = {Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces},
    journal = {The Visual Computer},
    year = {1996},
    volume = {12},
    pages = {527--545}
}

 @inproceedings{Kajiya82,
 author = {Kajiya,, James T.},
 title = {Ray tracing parametric patches},
 booktitle = {SIGGRAPH '82: Proceedings of the 9th annual conference on Computer graphics and interactive techniques},
 year = {1982},
 isbn = {0-89791-076-1},
 pages = {245--254},
 location = {Boston, Massachusetts, United States},
 doi = {http://doi.acm.org/10.1145/800064.801287},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

@inproceedings{Kalra89,
 author = {Kalra,, D. and Barr,, A. H.},
 title = {Guaranteed ray intersections with implicit surfaces},
 booktitle = {SIGGRAPH '89: Proceedings of the 16th annual conference on Computer graphics and interactive techniques},
 year = {1989},
 isbn = {0-201-50434-0},
 pages = {297--306},
 doi = {http://doi.acm.org/10.1145/74333.74364},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

 @article{Kanamori08,
  author    = {Yoshihiro Kanamori and
               Zoltan Szego and
               Tomoyuki Nishita},
  title     = {GPU-based Fast Ray Casting for a Large Number of Metaballs},
  journal   = {Comput. Graph. Forum},
  volume    = {27},
  number    = {2},
  year      = {2008},
  pages     = {351-360},
  ee        = {http://dx.doi.org/10.1111/j.1467-8659.2008.01132.x},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@INPROCEEDINGS{Knoll07,
    author = {Aaron Knoll and Ingo Wald},
    title = {Interactive Ray Tracing of Arbitrary Implicit Functions},
    booktitle = {Proceedings of the 2nd IEEE/EG Symposium on Interactive Ray Tracing},
    year = {2007},
    pages = {11--18}
}

@article {Knoll09,
  author = {Aaron Knoll and Y. Hijazi and Andrew Kensler and M. Schott and C. Hansen and H. Hagen},
  journal = {Comput. Graph. Forum},
  number = {1},
  pages = {26-40},
  title = {Fast Ray Tracing of Arbitrary Implicit Surfaces with Interval and Affine Arithmetic.},
  url = {http://dblp.uni-trier.de/db/journals/cgf/cgf28.html#KnollHKSHH09},
  volume = {28},
  year = {2009},
  ee = {http://dx.doi.org/10.1111/j.1467-8659.2008.01189.x},
  date = {2009-02-25}
}

@article{Kobbelt04,
  author    = {Leif Kobbelt and Mario Botsch},
  title     = {A survey of point-based techniques in computer graphics},
  journal   = {Computers {\&} Graphics},
  volume    = {28},
  number    = {6},
  year      = {2004},
  pages     = {801-814},
  ee        = {http://dx.doi.org/10.1016/j.cag.2004.08.009},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
 @inproceedings{Loop06,
 author = {Loop,, Charles and Blinn,, Jim},
 title = {Real-time GPU rendering of piecewise algebraic surfaces},
 booktitle = {SIGGRAPH '06: ACM SIGGRAPH 2006 Papers},
 year = {2006},
 isbn = {1-59593-364-6},
 pages = {664--670},
 location = {Boston, Massachusetts},
 doi = {http://doi.acm.org/10.1145/1179352.1141939},
 publisher = {ACM},
 address = {New York, NY, USA},
 }


@article {Lorensen87,
 author = {Lorensen,, William E. and Cline,, Harvey E.},
 title = {Marching cubes: A high resolution 3D surface construction algorithm},
 journal = {SIGGRAPH Comput. Graph.},
 volume = {21},
 number = {4},
 year = {1987},
 issn = {0097-8930},
 pages = {163--169},
 doi = {http://doi.acm.org/10.1145/37402.37422},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

 @inproceedings{Mitchell90,
 author = {Mitchell,, D. P.},
 title = {Robust ray intersection with interval arithmetic},
 booktitle = {Proceedings on Graphics interface '90},
 year = {1990},
 pages = {68--74},
 location = {Halifax, Nova Scotia},
 publisher = {Canadian Information Processing Society},
 address = {Toronto, Ont., Canada, Canada},
 }

 @ARTICLE{Mrken07,
    author = {Knut M{\o}rken and Martin Reimers},
    title = {An unconditionally convergent method for computing zeros of splines and polynomials},
    journal = {Math. Comp.},
    year = {2007},
    volume = {76},
    pages = {845--865}
}

@inproceedings{Nishita90,
 author = {Nishita,, Tomoyuki and Sederberg,, Thomas W. and Kakimoto,, Masanori},
 title = {Ray tracing trimmed rational surface patches},
 booktitle = {SIGGRAPH '90: Proceedings of the 17th annual conference on Computer graphics and interactive techniques},
 year = {1990},
 isbn = {0-201-50933-4},
 pages = {337--345},
 location = {Dallas, TX, USA},
 doi = {http://doi.acm.org/10.1145/97879.97916},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

@article {Nvid08,
    AUTHOR = {NVIDIA},
    TITLE = {CUDA SDK 2.0},
    YEAR = {2008},
    NOTE = {\httpAddr{//developer.nvidia.com/object/cuda.html}}}

@INPROCEEDINGS {Pabst06,
 author = {Pabst,, H.-F. and Springer,, J. P. and  Schollmeyer,, A. and Lenhardt,, R. and Lessig,, C. and Froehlich,, B.},
 title = {Ray Casting of Trimmed NURBS Surfaces on the GPU},
 booktitle = {Proceedings of IEEE Symposium on Interactive Ray Tracing 2006},
 year = {2006},
 isbn = {1-4244-0693-5},
 pages = {151-160},
 doi = {10.1109/RT.2006.280226},
 address = {Salt Lake City, UT, USA},
}

@article{Patrikalakis89,
  author    = {Nicholas M. Patrikalakis and George A. Kriezis},
  title     = {Representation of piecewise continuous algebraic surface in terms of B-splines},
  journal   = {The Visual Computer},
  volume    = {5},
  number    = {6},
  year      = {1989},
  pages     = {360-374},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@article{Reimers08,
  author    = {Martin Reimers and
               Johan Seland},
  title     = {Ray Casting Algebraic Surfaces using the Frustum Form},
  journal   = {Comput. Graph. Forum},
  volume    = {27},
  number    = {2},
  year      = {2008},
  pages     = {361-370},
  ee        = {http://dx.doi.org/10.1111/j.1467-8659.2008.01133.x},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@book{Salmon12,
author      = {George Salmon},
title       = {Analytic Geometry of Three Dimensions},
publisher   = {Longmans, Green and Co.},
year        = {1912}
}

@article{Sederberg85,
title = "Piecewise algebraic surface patches",
journal = "Computer Aided Geometric Design",
volume = "2",
number = "1-3",
pages = "53 - 59",
year = "1985",
note = "",
issn = "0167-8396",
doi = "DOI: 10.1016/0167-8396(85)90007-X",
url = "http://www.sciencedirect.com/science/article/B6TYN-45FKS4W-7/2/320aac774510f2308c1cda6328921853",
author = "Thomas W. Sederberg",
keywords = "Algebraic surfaces",
keywords = "solid modelling"
}

 @article{Seder88,
 author = {Sederberg, Thomas W. and Meyers, Ray J.},
 title = {Loop detection in surface patch intersections},
 journal = {Comput. Aided Geom. Des.},
 volume = {5},
 number = {2},
 year = {1988},
 issn = {0167-8396},
 pages = {161--171},
 doi = {http://dx.doi.org/10.1016/0167-8396(88)90029-5},
 publisher = {Elsevier Science Publishers B. V.},
 address = {Amsterdam, The Netherlands, The Netherlands},
 }

@INPROCEEDINGS {Sederberg89,
 author = {Sederberg,, Thomas W. and Zundel,, Alan K.},
 title = {Scan line display of algebraic surfaces},
 booktitle = {SIGGRAPH '89: Proceedings of the 16th annual conference on Computer graphics and interactive techniques},
 year = {1989},
 isbn = {0-201-50434-0},
 pages = {147--156},
 doi = {http://doi.acm.org/10.1145/74333.74348},
 publisher = {ACM},
 address = {New York, NY, USA},
}

@article{Sederberg96,
title = "Pyramids That Bound Surface Patches",
journal = "Graphical Models and Image Processing",
volume = "58",
number = "1",
pages = "75 - 81",
year = "1996",
note = "",
issn = "1077-3169",
doi = "DOI: 10.1006/gmip.1996.0005",
url = "http://www.sciencedirect.com/science/article/B6WG4-45MGYPS-1M/2/6d551e4839bd341d422be637ef790bdc",
author = "Thomas W. Sederberg and Alan K. Zundel"
}

@article{Shou06,
author = {Shou,, Huahao and Lin,, Hongwei and Martin,, Ralph R. and Wang,, Guojin},
 title = {Modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting},
 journal = {J. Comput. Appl. Math.},
 volume = {195},
 number = {1},
 year = {2006},
 issn = {0377-0427},
 pages = {155--171},
 doi = {http://dx.doi.org/10.1016/j.cam.2005.08.003},
 publisher = {Elsevier Science Publishers B. V.},
 address = {Amsterdam, The Netherlands, The Netherlands},
}


 @INCOLLECTION{Alberti05,
  AUTHOR =       {Lionel Alberti and G. Comte and Bernard Mourrain},
  TITLE =        {Meshing implicit algebraic surfaces: The smooth case},
  BOOKTITLE =    {Mathematical Methods for Curves and Surfaces: Troms{\o}'04},
  PUBLISHER =    {Nashboro.},
  YEAR =         {2005},
  isbn =         {0-9728482-4-X},
  editor =       {L.L. Schumaker and M. M{\ae}hlen and K. M{\o}rken},
  pages =        {11--26},
  address =      {Troms{\o} Norway}
}

@inproceedings{Barton97,
 author = {Stander, Barton T. and Hart, John C.},
 title = {Guaranteeing the topology of an implicit surface polygonization for interactive modeling},
 booktitle = {SIGGRAPH '97: Proceedings of the 24th annual conference on Computer graphics and interactive techniques},
 year = {1997},
 isbn = {0-89791-896-7},
 pages = {279--286},
 doi = {http://doi.acm.org/10.1145/258734.258868},
 publisher = {ACM Press/Addison-Wesley Publishing Co.},
 address = {New York, NY, USA},
 }

 @article{Alberti09,
title = "Isotopic triangulation of a real algebraic surface",
journal = "Journal of Symbolic Computation",
volume = "44",
number = "9",
pages = "1291 - 1310",
year = "2009",
note = "Effective Methods in Algebraic Geometry",
issn = "0747-7171",
doi = "DOI: 10.1016/j.jsc.2008.02.007",
url = "http://www.sciencedirect.com/science/article/B6WM7-4VKXC22-B/2/7d2a94fff45c0a9e864be3bb05507e7c",
author = "Lionel Alberti and Bernard Mourrain and Jean-Pierre T\'{e}court",
}

 @book{Patri02,
 author = {Patrikalakis, Nicholas M. and  Takashi Maekawa},
 title = {Shape Interrogation for Computer Aided Design and Manufacturing},
 year = {2002},
 isbn = {3540424547},
 publisher = {Springer-Verlag New York, Inc.},
 address = {Secaucus, NJ, USA},
 }

 @article{Singh10,
 author = {Singh, Jag Mohan and Narayanan, P. J.},
 title = {Real-Time Ray Tracing of Implicit Surfaces on the GPU},
 journal = {IEEE Transactions on Visualization and Computer Graphics},
 volume = {16},
 number = {2},
 year = {2010},
 issn = {1077-2626},
 pages = {261-272},
 doi = {http://dx.doi.org/10.1109/TVCG.2009.41},
 publisher = {IEEE Educational Activities Department},
 address = {Piscataway, NJ, USA},
 }

 @phdthesis{Spencer94,
 author = {Spencer, Melvin R.},
 title = {Polynomial real root finding in Bernstein form},
 year = {1994},
 order_no = {UMI Order No. GAX94-23360},
 school = {Brigham Young University},
 address = {Provo, UT, USA},
 }

@article{Rockwood89,
 author = {Rockwood, Alyn and Heaton, Kurt and Davis, Tom},
 title = {Real-time rendering of trimmed surfaces},
 journal = {SIGGRAPH Computer Graphics},
 volume = {23},
 number = {3},
 year = {1989},
 issn = {0097-8930},
 pages = {107-116},
 doi = {http://doi.acm.org/10.1145/74334.74344},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

@inproceedings{Witkin94,
 author = {Witkin, Andrew P. and Heckbert, Paul S.},
 title = {Using particles to sample and control implicit surfaces},
 booktitle = {SIGGRAPH '94: Proceedings of the 21st annual conference on Computer graphics and interactive techniques},
 year = {1994},
 isbn = {0-89791-667-0},
 pages = {269--277},
 doi = {http://doi.acm.org/10.1145/192161.192227},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

@article {Juttler02,
   author = {J\"{u}ttler, Bert and Felis, Alf},
   title = {Least-Squares Fitting of Algebraic Spline Surfaces},
   journal = {Advances in Computational Mathematics},
   publisher = {Springer U.S.},
   issn = {1019-7168},
   keyword = {Computer Science},
   pages = {135-152},
   volume = {17},
   issue = {1},
   url = {http://dx.doi.org/10.1023/A:1015200504295},
   note = {10.1023/A:1015200504295},
   year = {2002}
}

@article {Tong06,
   author = { Weihua Tong and Yuyu Feng and Falai Chen},
   title = {Hierarchical Implicit Tensor-Product B-Spline Surface and Its Application in Surface Reconstruction},
   journal = {Journal of Software},
   issn = {1000-9825},
   pages = {11-20},
   volume = {17},
   year = {2006}
}

@article{Wyvill86,
    abstract = {We introduce the concept ofsoft objects whose shape changes in response to their surroundings. Established geometric modelling techniques exist to handle most engineering components, including 'free form' shapes such as car bodies and telephones. More recently, there has been a lot of interest in modelling natural pheomena such as smoke, clouds, mountains and coastlines where the shapes are described stochastically, or as fractals. None of these techniques lends itself to the description ofsoft objects. This class of objects includes fabrics, cushions, living forms, mud and water. In this paper, we describe a method of modelling such objects and discuss its uses in animation. Our method is to represent asoft object, or collection of objects, as a surface of constant value in a scalar field over three dimensions. The main technical problem is to avoid calculating the field value at too many points. We do this with a combination of data structures at some cost in internal memory usage.},
    author = {Wyvill, Geoff and McPheeters, Craig and Wyvill, Brian},
    journal = {The Visual Computer},
    month = {August},
    number = {4},
    pages = {227--234},
    title = {Data structure for soft objects},
    volume = {2},
    year = {1986}
}

@article{Maekawa93,
title = "Computation of singularities and intersections of offsets of planar curves",
journal = "Computer Aided Geometric Design",
volume = "10",
number = "5",
pages = "407-429",
year = "1993",
note = "",
issn = "0167-8396",
doi = "DOI: 10.1016/0167-8396(93)90020-4",
url = "http://www.sciencedirect.com/science/article/B6TYN-45D9TTR-17/2/f66916108dd0c2419cfb7f3ecc6f20b1",
author = "Takashi Maekawa and Nicholas M. Patrikalakis",
keywords = "Offset curves",
keywords = "cusps",
keywords = "self-intersections",
keywords = "trimmed offsets",
keywords = "nonlinear equations",
keywords = "rounded interval arithmetic",
keywords = "subdivision."
}
